and sorry last point as you suggest if the delta is about to kill you which seems very unlikely, as you say because you are not paying up for a lot of ridiculously priced vega since its miles away closing out some of the put is fine
Sorry, it's totally unclear what you are trying to say. Are you comparing fixed-delta limit vs fixed interval hedging? In that case I have to disagree with you, hedging to some exposure limit with a hysteresis band is probably the best thing one can do in absence of an alpha strategy for the underlying. In delta-hedging, you have a lot knobs that you can turn to get a desired result - the hedging frequency, limit model, implied vol used to calculate deltas, how you include the dynamics of the implied vol in your delta calculations etc. While it's fun to discuss all these, your real-life impact will be mostly from your (a) realized vol spot-vol correlation, (b) realized autocorrelation of the underlying and (c) transaction costs. The rest are going to be secondary effects at best.
yeah im saying fixed delta is terrible fixed time is okay but wont remove the original problem of what if it moves a lot and the pnl looks down. the implied vol thing really isn't an issue because we aren't saying if only i could get the right vol im good. what is hysteresis bounds i never heard of this?
Could you elaborate why do you think fixed delta limit (i.e. hedging when your delta exceeds a limit) is worse than hedging at fixed time intervals (i.e. observing delta say every day and covering it)? Well, your hedging results change a lot depending on what volatility you are using to calculate your deltas. There are two key variables - how does the hedging implied vol relate to the expected realized vol and how often do you change it. There are literally hundreds of papers written about which approach is the best for what type of trading. Hysteresis band, not bound. It's a general idea where instead of fully acting on your signal you create a minimal threshold and you act after passing that threshold and only to that threshold.
thank you interesting. the only papers i've really read which sound similar require you to assume a utility function to then derive results about optimum bounds. on point one the fixed delta v fixed time interval. we agree that in the classic bs set up we can start with time as discretised and that roughly speaking if i increase the frequency of time sampling i decrease the variance of the value of the option+delta whilst leaving the expected change in value the same. again very non rigorously because of special properties of these processes we are able to use a limit argument to move to continuous time where we have no dependance on the spot path. amazingly this also gives a robust approach to trading and pricing options in terms of only the volatility in discrete time where you can be sure to realize profits or loses very roughly proportional to the difference in vol weighted by the average gamma you realise over the spot path but certainly positive if realised vol is higher than where u traded and u are long. if you instead assume black sholes and so delta is well defined and then discretize time and hedge at the boundaries there doesn't seem to me a reason why you would expect to keep the same expected return if you now hedge at stopping times which are non random functions derived from a model which we are violating instead of random times. this is v non rigorous but i think the effect is so massive it should be taken seriously. the reason its nice to hedge with delta bounds of course is unlike a lognormal browian motion we can't bound in any way the spot path by decreasing the time interval even though its fine 99.9% of the time so we can't use discrete time intervals. Point two i definitely agree the vol you hedge at matters to the pnl you realise for example if i am short a put and it crashes and i mark my vols up and hedge i sell a lot more than if i left them and do a lot worse. However i don't think discussions about properties of the vol surface dynamics either for the purposes of accounting or pricing or in relation to matching the real world have anything to do with this. very interested to hear any thoughts.
Still watching how a 271.5 Nov 16 straddle would be doing since 11-2. With hedging band around ~30 deltas looks like we'd add about 45 deltas yesterday. And a few more today. Straddle went from $875 extrinsic to $125. About -$220 on the straddle but +$120 offset from the hedge. Been very helpful to read the comments in concert with keeping an eye on how a real occurrence plays out. Looking forward to seeing how remaining value bleeds away as we get closer to expiration and also how all the values fluctuate if we get to see some price move back toward strike after putting on some hedge. Still feel pretty far from designing a strategy or system with options dynamics, but getting a better sense for how the things move has been interesting and helpful.
why does this work better? I would think it would work better when the underlying is mean reverting. If the asset is trending, you would want to over hedge (assuming we are short gamma). The reason I ask is, Bloomberg recently released their 10 day IVOL 100% moneyness (at least for my subscription) and I compared the SPX (IVOL10 - YangZ10 lagged 10 days)/IVOL10 for the past 10 years. On average, IVOL10 is 11% higher than what is realized with a median premium of 15%. Assuming efficient delta hedging and low transaction costs, systematically long flys (10 dte) seem like a valid idea for someone without upper management. I have also noticed that tick vol and 1 min vol is at a premium to daily vol (realized)for the spx (looking at the past 6 months, thats all the tick data I could find), do you have any tips on hedging to lock in the lowest volatility and how your hedging strategy may change depending on days until expiration? I thought going flat deltas EOD was good enough, but for short dated options (> 10 dte) the PnL is a bit to volatile.
I don't think that modeling intraday vol on 1min bars is a good idea. The general consensus of opinion is that estimates of vol on anything less than five minute bars is unreliable due to Epps Effect and ACF structure. Lots of papers on this, optimal seems to be between 5 and 15 minutes for vol estimation. See in particular Gatheral's Oxford-Man Rough Volatility site (which, I think, has Python code posted). I'm not sure how reliable SPX tick data is, since SPX is not actually a traded instrument. The intraday SPX data put out by Standard & Poors is (last I checked) calculated on last trade (and before 2016 did not even count non-listing market trades) which induces both lag and auto-correlation (due to non-traded effect). Maybe the Bloomberg SPX data is calculated from current bid/ask mid, but even then you'd still have the Epps effect. In short, I recommend moving to five minute vol estimates, or, for SPX, just use the Oxford-Man rough vol spx estimates, which are updated daily on that site.
Great resource!!! Going through some of his articles. https://tpq.io/p/rough_volatility_with_python.html I downloaded the csv files he provides for multiple indexes with multiple realized vol calcs. If his RV.Kernal model suggested the past 10 days SPX realized 10vol and over the same time period I hedged every hour(flattening my deltas) should I realize something similar to his 5min Kernal model? Or would I have to modify my hedging strategy to realize something closer to his model (assuming I could only hedge < once every hour)?